ZBT的计算几何模板

Basic template

一个基础型模板包括一个向量的实现

DATE: 2015-06-01

#define op operator
#define __ while
#define _0 return
typedef long long ll;
inline ll _(ll a,ll b){ll t;__(a){t=a;a=b%a;b=t;}_0 b;}
struct frac{
	ll u,d;
	frac(ll u=0,ll d=1):u(u),d(d){}
	frac op()(){ll _1=_(u,d);_0 frac(u/_1,d/_1);}
	frac op*(frac b){_0 (frac(u*b.u,d*b.d))();}
	frac op/(frac b){_0 (frac(u*b.d,d*b.u))();}
	frac op*(ll n){_0 (frac(u*n,d))();}
	frac op/(ll n){_0 (frac(u,d*n))();}
	frac op[](ll n){_0 frac(u*n,d*n);}
	frac op+(ll n){_0 frac(u+d*n,d);}
	frac op-(ll n){_0 frac(u-d*n,d);}
	frac op+(frac b){frac _1=(*this)[b.d],_2=b[d];_0 (frac(_1.u+_2.u,_1.d))();}
	frac op-(frac b){frac _1=(*this)[b.d],_2=b[d];_0 (frac(_1.u-_2.u,_1.d))();}
	void op=(ll b){d=1,u=b;}
	ll op()(frac b){return u*b.d-d*b.u;}//<=>
	bool op==(frac b){return u==b.u&&d==b.d;}
	bool op>(frac b){return b(*this)<0;}
	bool op<(frac b){return b(*this)>0;}
};
frac op/(ll a,frac b){_0 (frac(b.d*a,b.u))();}
frac op-(ll a,frac b){_0 frac(a)-b;}
frac op+(ll a,frac b){_0 frac(a)+b;}
frac op*(ll a,frac b){_0 (frac(a*b.u,b.d))();}
typedef struct vec{
	frac x,y;
	vec(frac x,frac y):x(x),y(y){};
	vec op+(vec b){_0 vec(x+b.x,y+b.y);}
	vec op-(vec b){_0 vec(x-b.x,y-b.y);}
	vec op*(frac b){_0 vec(x*b,y*b);}
	vec op/(frac b){_0 vec(x/b,y/b);}
	vec op*(ll b){_0 vec(x*b,y*b);}
	vec op/(ll b){_0 vec(x/b,y/b);}
	frac op*(vec b){_0 x*b.y-y*b.x;}//cross product
	frac op[](vec b){_0 x*b.x+y*b.y;}//dot product
	bool op==(vec b){_0 x==b.x&&y==b.y;}//equality test
} point;

本模板风格可能引起不适>_<

其实,用'[]'做dot product是因为C++中无法重载'.'运算符,而在大多数动态语言(比如javascript)中'.'与'[]'的作用几乎相等,且在javascript中'.'是一个'[]'的语法糖.

frac里就直接乱凑剩下的符号了>_<

有错误的话请提出来>_<...

Polygon & convex hull

Andrew法凸包.

#include <cstdio>
#include <malloc.h>
#include <cstring>
#include <algorithm>
#define op operator
#define __ while
#define _0 return
typedef long long ll;
using namespace std;
inline ll _(ll a,ll b){ll t;__(a){t=a;a=b%a;b=t;}_0 b;}
struct frac{
	ll u,d;
	frac(ll u=0,ll d=1):u(u),d(d){}
	frac op()(){ll _1=_(u,d);if(d/_1<0)_1=-_1;_0 frac(u/_1,d/_1);}
	frac op*(frac b){_0 (frac(u*b.u,d*b.d))();}
	frac op/(frac b){_0 (frac(u*b.d,d*b.u))();}
	frac op*(ll n){_0 (frac(u*n,d))();}
	frac op/(ll n){_0 (frac(u,d*n))();}
	frac op[](ll n){_0 frac(u*n,d*n);}
	frac op+(ll n){_0 frac(u+d*n,d);}
	frac op-(ll n){_0 frac(u-d*n,d);}
	frac op+(frac b){frac _1=(*this)[b.d],_2=b[d];_0 (frac(_1.u+_2.u,_1.d))();}
	frac op+(frac b){frac _1=(*this)[b.d],_2=b[d];_0 (frac(_1.u-_2.u,_1.d))();}
	void op=(ll b){d=1,u=b;}
	ll op()(frac b){return u*b.d-d*b.u;}//<=>
	bool op==(frac b){return u==b.u&&d==b.d;}
}
frac op/(ll a,frac b){_0 (frac(b.d*a,b.u))();}
frac op-(ll a,frac b){_0 frac(a)-b;}
frac op+(ll a,frac b){_0 frac(a)+b;}
frac op*(ll a,frac b){_0 (frac(a*b.u,b.d))();}
typedef struct vec{
	frac x,y;
	vec(frac x,frac y):x(x),y(y){};
	vec op+(vec b){_0 vec(x+b.x,y+b.y);}
	vec op-(vec b){_0 vec(x-b.x,y-b.y);}
	vec op*(frac b){_0 vec(x*b,y*b);}
	vec op/(frac b){_0 vec(x/b,y/b);}
	vec op*(ll a){_0 vec(x*b,y*b);}
	vec op/(ll b){_0 vec(x/b,y/b);}
	frac op*(vec b){_0 x*b.y-y*b.x;}//cross product
	frac op[](vec b){_0 x*b.x+y*b.y;}//dot product
	bool op==(vec b){_0 x==b.x&&y==b.y;}//equality test
} point;
bool pcmp(const point& p1,const point& p2){
	ll a=p1.x(p2.x);
	if(a>0) return false;
	if(a<0) return true;
	return p1.y(p2.y)<0;
}
struct polygon{
	point* p;
	int n,s;
	polygon(int k,point* q){
		s=(n=k)<<1;
		p=(point*)malloc(s*sizeof(point));
		for(int i=0;i<n;++i) p[i]=q[i];
	}
	inline void sizeup(int q){
		s<<=1;
		if(s>q){
			free(p);
			p=(point*)malloc(s*sizeof(point));
		}
	}
	inline void copy(polygon a){
		while(a.n>s){
			sizeup(a.n);
		}
		n=a.n;
		for(int i=0;i<n;++i) p[i]=a.p[i];
	}
	void op=(polygon a){
		copy(a);
	}
	void op=(polygon* a){
		copy(*a);
	}
	frac area(){
		frac area(0,1);
		for(int i=1;i<n-1;++i) area+=(p[i]-p[0])*(p[i+1]-p[0]);
		return area/2;
	}
	void sort(){
		sort(p,p+n,pcmp);
	}
}
struct convex_hull{
	polygon pol;//convex hull is also a polygon
	convex_hull(polygon* x){
		pol=x;
		polygon pol2=x;
		pol2.sort();
		int m=0;
		for(int i=0;i<pol2.n;++i){
			while(m>1 && ((pol.p[m-1]-pol.p[m-2])*(pol2.p[i]-pol.p[m-2]))(frac(0,1))<0ll) m--;
			pol.p[m++]=pol2.p[i];
		}
		int k=m;
		for(int i=pol2.n-2;~i;--){
			while(m>1 && ((pol.p[m-1]-pol.p[m-2])*(pol2.p[i]-pol.p[m-2]))(frac(0,1))<0ll) m--;
			pol.p[m++]=pol2.p[i];
		}
		if(pol2.n>1) m--;
		pol.n=m;
	}
}
int main(){
	return 0;
}

直接convex_hull(polygon)就求好凸包了>_<

凸包就是一个多边形嘛,就是凸的>_<